The dynamic propagation of an interface crack between two functionally graded material (FGM) layers under anti-plane shear is analyzed using the integral transform method. The properties of the FGM layers vary continuously along their thicknesses. The properties of the two FGM layers vary and the two layers are connected weak-discontinuously. A constant velocity Yoffe-type moving crack is considered. The Fourier transform is used to reduce the problem to a dual integral equation, which is then expressed to a Fredholm integral equation of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGM to show the effect of the gradient of material properties, crack moving velocity, and thickness of FGM layers. The following are helpful to increase resistance to interface crack propagation in FGMs: a) increasing the gradient of material properties, b) an increase of shear modulus and density from the interface to the upper and lower free surface, and c) increasing the thickness of the FGM layer. The DERR increases or decreases with increase of the crack moving velocity.